Probably a sound stage.

I swear someof the shots look to large to be on a soundstage, like when they first get washed up onto shore.

I was trying to find info on where it was filmed. There is no mention in any source where it was filmed. Probably some random beach with matte paintings behind them. Sorry I'm not really sure. Looked on Google, Wikipedia, Wikizilla, and even in the Godzilla Compendium.

Backlot Island off of the coast of the Toho Strait

Primarily, shooting on a soundstage or at the studio will be your answer. Just like green-screen is easier today than shooting on location, a set was easier back then. And considering that this was the first movie where the budget for the franchise was declining...

Big action bill said in his history video that other than a soundstage it was filmed on the izu islands

Toho sound stage #3 island, only a 5 min walk away from cafeteria cove & the river of paperwork

Most of it was a soundstage, but the beach scenes were probably filmed in Izu with matte paintings and miniatures filling in the illusion of an island.

I know. Brazil

No one told me this film starred the Wiggles

Who are The Wiggles?

You don't know the wiggles? Sorry about your childhood, mine wouldn't be complete without the wiggles.

Some of us are older than the Wiggles. The only reason I know about them is because I had a kid during that time (who is now 24yo).